When n number of particles each of mass m are at distances x_(1)=1, x_(2)=2, x_(3)=3, ………., x_(n)=n units from origin on the x-axis, then find the distance of their centre of mass from origin.

When n number of particles each of mass m are at distances x_(1)=1, x_

1.	When n number of particles each of mass m are at distances x_(1)=1, x_(2)=2, x_(3)=3, ………., x_(n)=n units from origin on the x-axis, then find the distance of their centre of mass from origin.
Answer» SOLUTION :`X_(CM)=(m(1)+m(2)+m(3)+…….+m(n))/(m+m+m+……+m("n terms"))` `=(m(1+2+3+………..+n))/(NM)=(m((n(n+1))/(2)))/(nm)=(n+1)/(2)`